you have one ticket, the odds of winning are 1/175,000,000.
you have two tickets, your odds are not 2/175,000,000.
your odds are 1/175,000,000 and 1/175,000,000
making it 2/325,000,000.
it's like when you flip a coin. you aren't going to get heads 5 times and tails 5 times. your chance is only for that specific instance, it doesn't carry over to the next flip. you don't get heads, and then the next flip your chance of getting tails increases/decreases by 10%. that is not how chance works.
1/10 + 1/10 = 2/10, not 2/20. You don't add the denominator together when doing addition. Always think of it as money when adding. 10 cents (1/10 of a dollar) plus 10 cents (1/10 of a dollar) gives you 20 cents (2/10 of a dollar).
The heads and tails logic does confuse a lot of people because it's multiplicative. Each event in isolation is a 50% chance of being the selected side. But if I wanted 3 heads in a row, that is multiplicative:
1/2 * 1/2 * 1/2 = 1/8 or a 12.5% chance of that happening, even if each event is a 50% chance in isolation.
none of this applies to something based off of random chance like the lottery.
you used a dollar as an example, but a dollar is a constant.